perf(data): absolute-space pyramid so acquire() is O(produced), not O(window)

Frame cost was O(capacity x levels) once the ring saturated: acquire() saw the
window base move (it always moves once the ring wraps), cleared the pyramid and
re-appended all 1,048,576 retained samples, and append() walked every live level
with no early stop -- 13,647,936 bucket merges and 73.8 ms per frame at a
1M-sample window, scaling with the window, which is what capped the 1 MS/s demo
at 32-58 ms/frame while it was still filling.

Index the pyramid in absolute bucket space instead. Level l bucket k covers the
samples [k * (kBucket << l), (k + 1) * (kBucket << l)), so a bucket's span never
depends on where the window starts and the window can slide over the aggregate
instead of forcing it to be rebuilt. Each level keeps its complete buckets in a
deque plus the absolute base of its first entry; append() folds a sample into the
single in-progress level-0 bucket and, only when that bucket completes, cascades
upward, stopping at the first level that gains no new entry; a new drop_before()
slides the window by discarding leading buckets and remembers where the window
begins. acquire() is now: drop to the new base, then append exactly what was
produced -- 256 merges and 0.034 ms per frame for 8192 new samples, independent
of the window, and memory bounded by the window (32,767 entries after 50M samples
through a 1M ring, the same as after 10M). A producer that laps the consumer by
more than capacity() between two acquires restarts the window rather than
splicing a gap.

Interface: `level(l) -> std::span<const MinMax>` cannot survive a ring and is
replaced by level_base/level_size/bucket in absolute bucket coordinates, plus
window_base/window_end/drop_before. The *_buckets queries stay in window
coordinates (index 0 = oldest retained sample), so Series keeps its window
semantics for callers; its exactness split now aligns in absolute space
(window_base() + the ceil/floor) because the bucket grid is absolute. The sums
move from per-level prefix sums to per-bucket ones -- the only representation a
sliding front can keep exact -- and StreamSeries::y_bounds() becomes
reduce(0, size()), exact in O(log n + kBucket) per frame instead of a scan of the
window. The pyramid owns the published window now, so there is no second copy of
base/end to keep in step, and gather() emits only buckets that are both complete
and wholly retained.

Tests: test-only merge counters (mirroring PLOT_PYRAMID_COUNT_COVERS, absent from
every non-test build) pin an acquire proportional to production and independent
of capacity, an append cost amortised over 16 live levels, and bounded memory;
brute-force checks pin absolute bucket aggregates across slides, sliding-window
reduce/sum/sumsq over unaligned ranges, and the level-1 gather mapping. The demo
now draws 946 samples/px at 1.03 ms/frame (967 fps) where the saturated window
cost 54.96 ms/frame (18 fps).

CMakeLists.txt

@@ -35,10 +35,12 @@ target_link_libraries(plot_core PRIVATE ${CMAKE_DL_LIBS})
 plot_apply_warnings(plot_core)
 
 if(PLOT_BUILD_TESTS)
-  # Test-only: counts the pyramid's covering-decomposition entries so a test can
-  # pin its O(log n) cost, which no query answer reveals. Off in every non-test
-  # build (see include/plot/data/detail/cover_count.hpp).
-  target_compile_definitions(plot_core PRIVATE PLOT_PYRAMID_COUNT_COVERS)
+  # Test-only: counts the pyramid's covering-decomposition entries and its bucket
+  # merges so a test can pin the query's O(log n) cost and the append path's
+  # amortised O(1) cost, neither of which any answer reveals. Off in every
+  # non-test build (see include/plot/data/detail/{cover,merge}_count.hpp).
+  target_compile_definitions(plot_core PRIVATE PLOT_PYRAMID_COUNT_COVERS
+                                             PLOT_PYRAMID_COUNT_MERGES)
 
   enable_testing()
   add_subdirectory(tests)

docs/superpowers/plans/2026-09-27-plot-library-scaffold.md

@@ -1063,12 +1063,20 @@ Take every quantity from `Series` (Task 3), never from the pyramid directly: `s.
 
 ```cpp
 struct PlotLayout {
-  Rect axes;        // plot area (excludes tick labels)
-  Rect y_label_area, x_label_area;
+  Rect axes;                       // plot area: excludes tick labels AND titles
+  Rect y_label_area, x_label_area; // one text line each, for tick labels
+  Rect y_title_area, x_title_area; // one text line each, for axis titles
   f32  y_axis_width   = 56.0f;
   f32  x_axis_height  = 22.0f;
+  f32  y_title_width  = 0.0f;      // set from the title's measured extent
+  f32  x_title_height = 0.0f;
 };
 ```
+`layout()` reserves one text line for tick labels and a second for the axis title on
+each occupied edge, and insets `axes` by all of them. A title drawn inside `axes`
+sits on top of the data and is a defect — the reserved strips exist to make that
+impossible rather than merely unlikely. An axis with no title reserves nothing.
+
 `Plot` owns vectors of axes/traces/cursors/measures, computes `PlotLayout` from `viewport()` and the text backend metrics, and recomputes measurement results for every measure whose cursors moved (dirty flag, not every frame).
 
 `Grid` produces tick-aligned line segments in data space; `Trace` binds a `Series` to a color/width/axis pair; `Cursor` carries `f64 x`, `SnapMode { Free, NearestSample }`, color and an optional label; `Annotation` is a pinned point with text.

docs/superpowers/specs/2026-09-27-plot-library-design.md

@@ -82,8 +82,19 @@ approach that fails at high sample rates.
 
 Vertex buffers hold raw *data* coordinates. Screen mapping is
 `x' = x * sx + tx`, `y' = y * sy + ty` evaluated in the vertex shader from a
-`Transform` uniform. Panning and zooming therefore touch one uniform and zero
-vertex data. Only new samples or an LOD-level change cause an upload.
+`Transform` uniform. The CPU never transforms a vertex, and a pan or zoom changes
+one uniform and no vertex *values*.
+
+The staged window is view-dependent: each frame the renderer gathers just the
+visible sample range (or the visible buckets of the chosen LOD level) and uploads
+it. That per-frame cost is **O(visible pixels)** — about two segments per pixel
+column, flat in series length — so the property this section exists for holds.
+A staging cache keyed on `(series, level, first, last, viewport)` would let a
+static plot skip the redundant gather and upload entirely; it is not implemented,
+because it changes no asymptotics and would add an invalidation surface (new
+samples, LOD changes, series mutation, streaming window slide) whose bugs are
+worse than the redundant work it removes. Recorded here as deliberate future
+work, not as a missing feature.
 
 Log axes are handled inside the same transform (`log10` before scaling) so no
 separate code path or pre-transformed buffer is needed.
@@ -94,8 +105,18 @@ Every series owns a mip chain: level 0 buckets `kBucket = 64` consecutive sample
 and stores one `(min, max)` pair per bucket; each subsequent level halves the
 bucket count. Memory cost is `n/8` bytes at level 0 (2 floats per 64 samples) times the geometric sum `1 + ½ + ¼ + …`, giving `n/4` bytes total — ≈6% of the 4n bytes of raw samples, not 2×.
 
-- Built incrementally: `append()` updates only the last bucket and the O(log n)
-  chain above it — amortised O(1) per sample.
+- Built incrementally, in **absolute bucket space**: level `l` bucket `k` covers
+  samples `[k · (kBucket << l), (k + 1) · (kBucket << l))`. A bucket's span
+  therefore never depends on where the current window starts, which is what lets a
+  window slide over a pyramid instead of forcing it to be rebuilt. `append()`
+  folds a sample into the single in-progress level-0 bucket and, exactly when that
+  bucket completes, pushes it and merges upward, stopping at the first level that
+  gains no new entry: level `l` gains one entry per `kBucket << l` samples, so an
+  append costs amortised O(1) (`1/kBucket + 1/(2·kBucket) + … = 2/kBucket` merges)
+  and never walks the live levels.
+- A sliding window (a `StreamSeries` ring) drops the leading buckets it no longer
+  holds and appends only the newly produced samples, so nothing is recomputed and
+  memory stays bounded by the retained window rather than the total ever pushed.
 - The renderer picks the level where samples-per-pixel ≈ 2, so a 100M-sample
   series rasterises ≈ `2 · viewport_width` vertices instead of 100M.
 - Buckets preserve extremes, so spikes are never dropped by decimation.
@@ -127,6 +148,12 @@ otherwise silently include samples outside the range. Exactness therefore lives
 on `Series` (which owns the raw samples), and `MinMaxPyramid` exposes only
 bucket-exact queries, named `*_buckets` so they cannot be mistaken for exact ones.
 
+The bucket grid is absolute while a sliding window's base is not, so that split is
+computed in absolute coordinates — `Series` asks the pyramid for `window_base()`
+and aligns `ceil`/`floor` there before mapping back to window indices. That is
+also how a stream's `y_bounds()` stays exact in O(log n + kBucket) per frame: it
+is `reduce(0, size())` over the window rather than a scan of it.
+
 ### 4.5 Decimation approach — decision
 
 | | Approach | Verdict |
@@ -196,9 +223,17 @@ namespace data {
   class MinMaxPyramid {
    public:
     void reserve(u64 n); void append(f32 v); void clear();
-    u64 size() const;
+    // Absolute bucket space: level l entry i covers the absolute samples
+    // [i * (kBucket << l), (i + 1) * (kBucket << l)). The window slides over the
+    // same buckets; queries are in window coordinates (index 0 = oldest retained).
+    void drop_before(u64 absolute_sample);
+    u64 size() const;                                        // retained window size
+    u64 window_base() const;                                 // abs index of index 0
+    u64 window_end() const;                                  // abs index past the last
+    u32 level_count() const;
+    u64 level_base(u32 l) const, level_size(u32 l) const;
+    MinMax bucket(u32 l, u64 absolute_bucket) const;
     u32 level_for(u64 n, f64 samples_per_pixel) const;
-    std::span<const MinMax> level(u32 l) const;
     u64 snap(f64 x, f64 x0, f64 dx) const;                   // nearest sample index
     // Whole-bucket only: aggregates over the level-0 buckets fully contained in
     // [begin, end). Partial edges are excluded, not approximated. Callers wanting
@@ -308,8 +343,17 @@ namespace input {
 - Producers write to `data::StreamSeries` from an acquisition thread through a
   lock-free SPSC ring. No mutex on the sample path.
 - A frame begins with `StreamSeries::acquire()`, which publishes a consistent
-  `[0, produced)` snapshot and extends the pyramid by exactly the newly produced
-  samples. Readers use the snapshot; the producer never blocks.
+  `[0, produced)` snapshot: it slides the pyramid's retained window to the new
+  base, dropping the leading buckets the ring has overwritten, then extends the
+  pyramid by exactly the newly produced samples. Its cost is **O(samples produced
+  since the last acquire)** — independent of both the window size and the series
+  length — and so is its memory, because the drops bound the pyramid to the
+  retained window instead of the total ever pushed. A frame's total cost is
+  therefore O(new samples + visible pixels), and no part of the frame path is
+  proportional to the window. The one exception is a producer that laps the
+  consumer by more than `capacity()` samples between two acquires: the samples in
+  between were never appended, so that acquire re-reads the retained window from
+  scratch. Readers use the snapshot; the producer never blocks.
 - `Renderer`, `Plot`, and `Controller` are confined to the render thread.
 
 ## 8. Error handling

include/plot/data/detail/merge_count.hpp

@@ -0,0 +1,31 @@
+#pragma once
+
+#ifdef PLOT_PYRAMID_COUNT_MERGES
+
+#include <atomic>
+
+#include <plot/core/types.hpp>
+
+namespace plot::data::detail {
+
+/// Test-only instrumentation. Counts the bucket merges the append path has
+/// performed since the counter was last reset: one for the bucket pushed at
+/// level 0 when it completes, plus one for every parent bucket written above it.
+///
+/// The append path's *cost* is invisible in every answer -- a pyramid that walks
+/// every live level per sample returns exactly the same min/max/sum as one that
+/// stops at the first level that gained no entry -- so a test that wants to pin
+/// "amortised O(1) per sample, independent of the number of live levels" has to
+/// count merges. The counter exists only when PLOT_PYRAMID_COUNT_MERGES is
+/// defined (the test build defines it), so every normal build carries no counter
+/// and no increment on the append path.
+///
+/// Not part of the query surface and not meant for production use.
+inline std::atomic<u64>& merge_count() {
+  static std::atomic<u64> count{0};
+  return count;
+}
+
+}  // namespace plot::data::detail
+
+#endif  // PLOT_PYRAMID_COUNT_MERGES

include/plot/data/minmax_pyramid.hpp

@@ -1,5 +1,5 @@
 #pragma once
-#include <span>
+#include <deque>
 #include <vector>
 
 #include <plot/core/types.hpp>
@@ -16,13 +16,33 @@ struct MinMax {
 /// series and the level maths is a shift.
 inline constexpr u32 kBucket = 64;
 
-/// Incremental min/max LOD pyramid.
+/// Incremental min/max LOD pyramid, indexed in absolute bucket space.
 ///
-/// Level 0 buckets kBucket consecutive samples and keeps one (min, max) per
-/// bucket; level l buckets 2^l level-0 buckets. Memory is n/4 bytes -- about 6%
-/// of 4-byte raw samples. append() merges into the last bucket at each level and
-/// walks up the O(log n) chain above it, so building is amortised O(1) per sample
-/// and nothing is ever recomputed from raw samples.
+/// Level `l` bucket `k` covers the absolute samples
+/// `[k * (kBucket << l), (k + 1) * (kBucket << l))`. Bucket boundaries are
+/// therefore fixed for the pyramid's whole life: appending never re-buckets an
+/// existing aggregate, and the window a caller reads can slide over the same
+/// buckets instead of being rebuilt from the raw samples.
+///
+/// Each level holds its complete buckets in a deque (O(1) push_back *and*
+/// pop_front) plus a `base`, the absolute level-`l` bucket index of its first
+/// entry. `append()` folds a sample into the in-progress level-0 bucket and, when
+/// that bucket completes, pushes it and walks up -- stopping at the first level
+/// that gains no new entry. Level `l` gains one entry per `kBucket << l` samples,
+/// so an append costs amortised O(1) and never walks every live level.
+///
+/// `drop_before(u)` slides the window's leading edge to absolute sample `u`: each
+/// level discards the buckets whose span starts before `u`, so the memory is
+/// bounded by the retained window (about n/4 bytes, ~6% of 4-byte raw samples)
+/// and not by the number of samples ever appended. Every stored entry is the
+/// complete aggregate of its own span and every stored span lies inside the
+/// retained window, so no aggregate is ever recomputed or invalidated.
+///
+/// Queries are in *window* coordinates: index 0 is the oldest retained sample,
+/// `size()` is the retained sample count, and `window_base()` is the absolute
+/// index window index 0 refers to. That is the same window `Series` publishes,
+/// which is why a `StreamSeries` can hand the pyramid a moving base and keep
+/// answering in its own coordinates.
 ///
 /// A pyramid stores *aggregates*, so it can only answer exactly for whole
 /// buckets; a range with partial edge buckets would silently pull in samples
@@ -30,23 +50,49 @@ inline constexpr u32 kBucket = 64;
 /// *_buckets, and exact range queries live on Series, which owns the raw samples.
 class MinMaxPyramid {
  public:
-  MinMaxPyramid() { add_level(); }
+  MinMaxPyramid() = default;
 
-  /// Sizes every level (buckets and prefix sums) for `n` samples so a following
-  /// run of appends performs no reallocation. The pyramid itself stays empty.
+  /// Sizes the level table for a window of `n` samples so a following run of
+  /// appends never grows the level vector. The bucket deques themselves grow in
+  /// chunks: a sliding window cannot know their final length up front.
   void reserve(u64 n);
   void append(f32 v);
+  /// Slides the retained window's leading edge to absolute sample index
+  /// `absolute_sample`, dropping every aggregate that covered a sample before it.
+  /// Monotonic for arguments ahead of the base; a no-op for arguments at or
+  /// behind it, and for an empty pyramid.
+  ///
+  /// An argument past `window_end()` (a producer that outran the consumer by more
+  /// than the ring held) drops everything and restarts the window there: the
+  /// samples in between were never appended, so they are not representable.
+  void drop_before(u64 absolute_sample);
   void clear();
 
-  u64 size() const noexcept { return size_; }
+  /// Samples in the retained window.
+  u64 size() const noexcept { return count_ - base_; }
+  /// Absolute index of the sample window index 0 refers to.
+  u64 window_base() const noexcept { return base_; }
+  /// Absolute index one past the last appended sample: the first sample index a
+  /// following append() will occupy.
+  u64 window_end() const noexcept { return count_; }
   /// At least 1, even when empty, so level_count() - 1 is always valid.
   u32 level_count() const noexcept { return live_levels_; }
-  /// Level `l`'s buckets; empty span when `l` is beyond level_count().
-  std::span<const MinMax> level(u32 l) const;
 
-  /// Min/max over the whole level-0 buckets fully contained in [begin, end).
-  /// Partial edge buckets are excluded, never approximated; an empty result is a
-  /// degenerate Range with span() == 0.
+  /// Absolute level-`l` bucket index of level `l`'s first entry, and how many
+  /// entries it holds. They cover `[level_base(l), level_base(l) + level_size(l))`:
+  /// entry `i` is the aggregate of the absolute samples
+  /// `[i * (kBucket << l), (i + 1) * (kBucket << l))`. A level that exists but
+  /// holds nothing, or a level past level_count(), reports size 0 (its base is
+  /// then meaningless).
+  u64 level_base(u32 l) const noexcept;
+  u64 level_size(u32 l) const noexcept;
+  /// Aggregate of the absolute level-`l` bucket `i`. Precondition:
+  /// level_base(l) <= i < level_base(l) + level_size(l).
+  MinMax bucket(u32 l, u64 i) const;
+
+  /// Min/max over the whole level-0 buckets fully contained in the window range
+  /// [begin, end). Partial edge buckets are excluded, never approximated; an
+  /// empty result is a degenerate Range with span() == 0.
   Range reduce_buckets(u64 begin, u64 end) const;
   /// Sum of the samples in those same whole buckets, accumulated in double.
   f64 sum_buckets(u64 begin, u64 end) const;
@@ -62,13 +108,32 @@ class MinMaxPyramid {
   u64 snap(f64 x, f64 x0, f64 dx) const;
 
  private:
-  void add_level();
+  /// One bucket: its extremes plus the raw-sum aggregates Series folds over.
+  struct Entry {
+    MinMax mm;
+    f64 sum = 0.0;
+    f64 sumsq = 0.0;
+  };
+  /// One level's complete buckets, in absolute bucket-index order.
+  struct Level {
+    std::deque<Entry> entries;
+    u64 base = 0;   ///< absolute level-l bucket index of entries.front()
+  };
 
-  u64 size_ = 0;
-  u64 reserved_n_ = 0;
+  void add_level();
+  /// Appends `e` at absolute level-`l` bucket `k`, which must be one past the
+  /// level's last entry.
+  void push(u32 l, u64 k, const Entry& e);
+  /// Entry for absolute level-`l` bucket `i`; the caller has checked the range.
+  const Entry& at(u32 l, u64 i) const {
+    return levels_[l].entries[static_cast<usize>(i - levels_[l].base)];
+  }
+
+  u64 count_ = 0;   ///< absolute index one past the last appended sample
+  u64 base_ = 0;    ///< absolute index of the window's oldest sample
   u32 live_levels_ = 1;
-  std::vector<std::vector<MinMax>> levels_;       // levels_[0] = kBucket granularity
-  std::vector<std::vector<f64>> sums_, sumsqs_;   // inclusive prefix sums per level
+  std::vector<Level> levels_{1};
+  Entry pending_;   ///< the in-progress level-0 bucket, not yet an entry
 };
 
 }  // namespace plot::data

include/plot/data/series.hpp

@@ -65,7 +65,9 @@ class Series {
     u64 left_begin = 0, left_end = 0;           // partial head bucket
     u64 right_begin = 0, right_end = 0;         // partial tail bucket
   };
-  static QueryParts split_query(u64 begin, u64 end);
+  /// Needs the pyramid's window base: the bucket grid it aligns to is absolute,
+  /// while begin/end are window coordinates.
+  QueryParts split_query(u64 begin, u64 end) const;
   /// Reads both edge spans through copy_raw() into `out` (which must hold at
   /// least 2*kBucket samples) and returns how many were written.
   u64 copy_edges(const QueryParts& parts, f32* out) const;

include/plot/data/stream_series.hpp

@@ -17,13 +17,16 @@ namespace plot::data {
 ///
 /// Indexing is the *retained window published by the last acquire()*: size(),
 /// reduce(), sum(), sumsq(), gather() and pyramid() all use it, and index 0 is
-/// the oldest sample still held. Once the producer has written more than
-/// capacity() samples the oldest ones are gone, so acquire() notices that the
-/// window's base moved and rebuilds the pyramid from the retained samples -- an
-/// incremental append would splice a dropped prefix onto a retained suffix and
-/// mis-align every bucket (bucket boundaries are absolute, not relative to the
-/// window). Until the ring saturates, acquire() is O(new samples); once it wraps,
-/// an acquire whose base moved costs O(capacity()).
+/// the oldest sample still held.
+///
+/// The pyramid behind those queries is indexed in absolute sample space, so a
+/// window that slides only makes it drop the leading buckets the ring has
+/// overwritten and append the samples produced since the last acquire(): acquire()
+/// costs O(samples produced), not O(capacity()), and the aggregates that stay in
+/// the window are never recomputed. The one exception is a producer that laps the
+/// consumer -- more than capacity() samples between two acquires -- where the
+/// samples in between were never appended and the pyramid restarts at the new
+/// base, so that acquire re-reads the whole window.
 ///
 /// x0() is therefore the x of the oldest retained sample, x_bounds().min == x0(),
 /// and y_bounds() covers exactly the published samples.
@@ -42,8 +45,9 @@ namespace plot::data {
 /// one of those k newer samples (or a still-newer sample, once the producer has
 /// lapped again) instead of the sample the snapshot names. Nothing else moves: the
 /// count, the absolute index -> x mapping and the newest end of the window are
-/// derived from the one published count, and the next acquire() rebuilds from the
-/// base it observes, so the pyramid never mixes two windows. Ingest with no reuse
+/// derived from one published count, and the next acquire() slides the pyramid's
+/// window to the base it observes (dropping the leading buckets, appending what is
+/// new), so the pyramid never mixes two windows. Ingest with no reuse
 /// underneath a read at all needs the producer to stop before unread data
 /// (drop-on-full) or a claim protocol, i.e. a different contract from the one this
 /// class specifies.
@@ -76,8 +80,9 @@ class StreamSeries final : public Series {
   RingBuffer<f32> ring_;
   f64 x0_ = 0.0;
   f64 dx_ = 1.0;
-  u64 base_ = 0;   // absolute index of retained index 0 in the published snapshot
-  u64 end_ = 0;    // absolute index one past the published snapshot
+  // The pyramid owns the published window: its window_base() is the absolute
+  // index of retained index 0 and its size()/window_end() are the snapshot's
+  // extent, so there is no second copy of that state to keep in step.
   MinMaxPyramid pyramid_;
   Range y_bounds_{};
 };

src/data/minmax_pyramid.cpp

@@ -1,8 +1,10 @@
 #include <plot/data/detail/cover_count.hpp>
+#include <plot/data/detail/merge_count.hpp>
 #include <plot/data/minmax_pyramid.hpp>
 
 #include <algorithm>
 #include <cmath>
+#include <cstddef>
 
 namespace plot::data {
 namespace {
@@ -16,18 +18,19 @@ constexpr u64 buckets_for(u64 n, u32 l) {
   return n / span + (n % span == 0 ? u64{0} : u64{1});
 }
 
+/// Ceiling division: first level-l bucket whose span starts at or after v.
+constexpr u64 ceil_div(u64 v, u64 d) { return v / d + (v % d == 0 ? u64{0} : u64{1}); }
+
 /// First level-0 bucket boundary at or after v.
-constexpr u64 ceil_to_bucket(u64 v) {
-  return (v / kBucket + (v % kBucket == 0 ? u64{0} : u64{1})) * kBucket;
-}
+constexpr u64 ceil_to_bucket(u64 v) { return ceil_div(v, kBucket) * kBucket; }
 
 /// Canonical, coarsest-first decomposition of the level-0 bucket span [b0, b1)
-/// into pyramid entries, calling fn(level, index) for each.
+/// into pyramid entries, calling fn(level, absolute_bucket_index) for each.
 ///
 /// A level-l entry is emitted only when the whole level-l bucket exists (all
 /// kBucket << l samples are present, so its aggregate is final). Callers
-/// guarantee b1 <= ceil(size() / kBucket), so the only possible remainder is the
-/// single trailing partial level-0 bucket, which is emitted at level 0.
+/// guarantee b0 >= the first whole bucket of the window and b1 <= the number of
+/// complete buckets, so every emission both exists and lies inside the window.
 ///
 /// The level is chosen per *emission*, not once per pass: at each cursor the
 /// largest level is taken whose bucket is aligned with the cursor, lies wholly
@@ -40,16 +43,18 @@ constexpr u64 ceil_to_bucket(u64 v) {
 /// no coarser level is ever reachable from an odd cursor.
 template <typename Fn>
 void cover_buckets(const MinMaxPyramid& p, u64 b0, u64 b1, Fn&& fn) {
-  const u64 complete = p.size() / kBucket;
-  const u64 limit = std::min(b1, complete);
+  // One past the last complete level-0 bucket: levels sit on top of those, so
+  // this also bounds every coarser bucket the cursor may take.
+  const u64 limit = std::min(b1, p.level_base(0) + p.level_size(0));
   const u32 top = p.level_count() - 1;         // level_count() is at least 1
   u64 b = b0;
   while (b < b1) {
     u32 li = top;
     for (;;) {
       const u64 lb = u64{1} << li;
-      if ((b % lb) == 0 && b + lb <= limit &&
-          (b / lb) < static_cast<u64>(p.level(li).size())) {
+      const u64 i = b >> li;
+      if ((b % lb) == 0 && b + lb <= limit && i >= p.level_base(li) &&
+          i - p.level_base(li) < p.level_size(li)) {
         break;
       }
       if (li == 0) break;
@@ -69,7 +74,7 @@ Range fold_range(const MinMaxPyramid& p, u64 b0, u64 b1) {
   Range r{};
   bool first = true;
   cover_buckets(p, b0, b1, [&](u32 l, u64 i) {
-    const MinMax m = p.level(l)[static_cast<usize>(i)];
+    const MinMax m = p.bucket(l, i);
     if (first) {
       r.min = f64(m.min);
       r.max = f64(m.max);
@@ -84,140 +89,170 @@ Range fold_range(const MinMaxPyramid& p, u64 b0, u64 b1) {
 
 }  // namespace
 
-void MinMaxPyramid::add_level() {
-  levels_.emplace_back();
-  sums_.emplace_back();
-  sumsqs_.emplace_back();
-}
+void MinMaxPyramid::add_level() { levels_.emplace_back(); }
 
 void MinMaxPyramid::reserve(u64 n) {
-  if (n > reserved_n_) reserved_n_ = n;
-  const u64 want = std::max(std::max(n, size_), u64{2});
+  // Materialise every level n samples can need -- level 0 plus one per doubling
+  // of the bucket -- so a run of appends never grows the level vector. See the
+  // header for why the bucket deques themselves cannot be pre-sized.
+  u32 want = 1;
+  for (u64 span = level_span(0); span <= n && want < 63; span <<= 1) ++want;
+  if (levels_.size() < want) levels_.resize(want);
+}
 
-  // Materialise every level n samples can need -- buckets *and* prefix sums --
-  // and size each one up front, so a run of appends allocates nothing at all.
-  u32 max_levels = 1;
-  for (u64 span = level_span(0); span <= want && max_levels < 63; span <<= 1) ++max_levels;
-  while (levels_.size() < max_levels) add_level();
-  for (u32 l = 0; l < levels_.size(); ++l) {
-    const usize want_l = static_cast<usize>(buckets_for(want, l));
-    levels_[l].reserve(want_l);
-    sums_[l].reserve(want_l);
-    sumsqs_[l].reserve(want_l);
-  }
+void MinMaxPyramid::push(u32 l, u64 k, const Entry& e) {
+  Level& lv = levels_[l];
+  // The first entry of a level fixes its base; every later entry is the next
+  // absolute bucket, which is what keeps a level one contiguous run.
+  if (lv.entries.empty()) lv.base = k;
+  lv.entries.push_back(e);
+#ifdef PLOT_PYRAMID_COUNT_MERGES
+  detail::merge_count().fetch_add(1, std::memory_order_relaxed);
+#endif
 }
 
 void MinMaxPyramid::append(f32 v) {
-  const u64 prev = size_;
   const f64 vd = f64(v);
-  // sum_[l].back() is the sum over every sample appended so far, and the newest
-  // sample always lands in the last bucket of every level, so the last prefix
-  // entry of every level is exactly the running total.
-  const f64 total_before = sums_[0].empty() ? 0.0 : sums_[0].back();
-  const f64 total = total_before + vd;
-  const f64 sq_before = sumsqs_[0].empty() ? 0.0 : sumsqs_[0].back();
-  const f64 total_sq = sq_before + vd * vd;
-
-  const u64 idx = prev / kBucket;
-  if (idx == levels_[0].size()) {
-    levels_[0].push_back(MinMax{v, v});
-    sums_[0].push_back(total);
-    sumsqs_[0].push_back(total_sq);
+  // The new sample always lands in the in-progress level-0 bucket, which is the
+  // only bucket any append ever touches: a bucket becomes an entry exactly once,
+  // complete, and is never rewritten.
+  if (count_ % kBucket == 0) {
+    pending_.mm.min = v;
+    pending_.mm.max = v;
+    pending_.sum = vd;
+    pending_.sumsq = vd * vd;
   } else {
-    MinMax& cur = levels_[0][static_cast<usize>(idx)];
-    cur.min = std::min(cur.min, v);
-    cur.max = std::max(cur.max, v);
-    sums_[0][static_cast<usize>(idx)] = total;
-    sumsqs_[0][static_cast<usize>(idx)] = total_sq;
+    pending_.mm.min = std::min(pending_.mm.min, v);
+    pending_.mm.max = std::max(pending_.mm.max, v);
+    pending_.sum += vd;
+    pending_.sumsq += vd * vd;
   }
+  ++count_;
+  if (count_ % kBucket != 0) return;   // the bucket is still partial: nothing to push
 
+  const u64 k0 = count_ / kBucket - 1;   // the level-0 bucket that just completed
+  if (k0 < level_base(0)) return;        // its span starts before the window: never read
+  const Entry done = pending_;
+  push(0, k0, done);
+
+  // Cascade: level l gains an entry exactly when kBucket << l divides the sample
+  // count, so the walk stops at the first level that gained nothing -- amortised
+  // O(1) per sample (1/kBucket + 1/(2*kBucket) + ... = 1/(kBucket/2) merges).
   for (u32 l = 1; l < 63; ++l) {
-    // A level only carries data once the level below has more than one bucket: a
-    // one-child parent would just duplicate it.
-    if (levels_[l - 1].size() < 2) break;
-    if (l == live_levels_) {
-      ++live_levels_;
-      if (l == levels_.size()) {   // no reserve() sized this level up front
-        add_level();
-        if (reserved_n_ != 0) {
-          const usize want = static_cast<usize>(buckets_for(reserved_n_, l));
-          levels_[l].reserve(want);
-          sums_[l].reserve(want);
-          sumsqs_[l].reserve(want);
+    const u64 span = level_span(l);
+    if (count_ % span != 0) break;
+    const u64 k = count_ / span - 1;        // the level-l bucket that just completed
+    const u64 child = 2 * k;                // its left child, at level l-1
+    if (child < level_base(l - 1)) break;   // a child is gone: this parent is not retained
+    if (l == static_cast<u32>(levels_.size())) add_level();
+    if (l >= live_levels_) live_levels_ = l + 1;
+    const Entry& a = at(l - 1, child);
+    const Entry& b = at(l - 1, child + 1);
+    Entry m;
+    m.mm.min = std::min(a.mm.min, b.mm.min);
+    m.mm.max = std::max(a.mm.max, b.mm.max);
+    m.sum = a.sum + b.sum;
+    m.sumsq = a.sumsq + b.sumsq;
+    push(l, k, m);
   }
+}
+
+void MinMaxPyramid::drop_before(u64 absolute_sample) {
+  if (absolute_sample <= base_) return;
+  if (absolute_sample > count_) {
+    // The producer produced more than the ring held between two acquires: every
+    // appended sample is gone and the ones in between were never appended, so the
+    // pyramid restarts empty at the new base rather than splicing a gap.
+    base_ = absolute_sample;
+    count_ = absolute_sample;
+    pending_ = Entry{};
+    live_levels_ = 1;
+    for (u32 l = 0; l < levels_.size(); ++l) {
+      levels_[l].entries.clear();
+      levels_[l].base = ceil_div(absolute_sample, level_span(l));
     }
+    return;
   }
-    const u64 ci = prev / level_span(l - 1);   // current bucket at level l-1
-    const u64 parent = ci / 2;                 // its parent at level l
-    MinMax m;
-    if ((ci & 1u) != 0) {
-      const MinMax& a = levels_[l - 1][static_cast<usize>(ci - 1)];
-      const MinMax& b = levels_[l - 1][static_cast<usize>(ci)];
-      m.min = std::min(a.min, b.min);
-      m.max = std::max(a.max, b.max);
+
+  base_ = absolute_sample;
+  for (u32 l = 0; l < levels_.size(); ++l) {
+    Level& lv = levels_[l];
+    // A bucket is dropped once its span starts before the window: the first
+    // retained bucket of every level is the first one wholly inside the window,
+    // which is exactly what the queries assume.
+    const u64 keep = ceil_div(base_, level_span(l));
+    if (keep <= lv.base) continue;
+    const u64 have = static_cast<u64>(lv.entries.size());
+    const u64 drop = std::min(keep - lv.base, have);
+    lv.entries.erase(lv.entries.begin(),
+                     lv.entries.begin() + static_cast<std::ptrdiff_t>(drop));
+    // The base is where the next entry goes: past the last one if the level was
+    // emptied, which is how the cursor catches up with the sliding window.
+    if (drop == have) {
+      lv.base = keep;
     } else {
-      m = levels_[l - 1][static_cast<usize>(ci)];
-    }
-    if (parent == levels_[l].size()) {
-      levels_[l].push_back(m);
-      sums_[l].push_back(total);
-      sumsqs_[l].push_back(total_sq);
-    } else {
-      levels_[l][static_cast<usize>(parent)] = m;
-      sums_[l][static_cast<usize>(parent)] = total;
-      sumsqs_[l][static_cast<usize>(parent)] = total_sq;
+      lv.base += drop;
     }
   }
-  size_ = prev + 1;
+  // The in-progress level-0 bucket may now start before the window's base: its
+  // aggregate covers samples that are gone. It belongs to the bucket the window
+  // starts inside, which is never read (the queries take whole buckets and the
+  // Series scans the two partial edges raw), so discarding it is lossless.
+  if (ceil_div(base_, kBucket) > count_ / kBucket) pending_ = Entry{};
+  while (live_levels_ > 1 && level_size(live_levels_ - 1) == 0) --live_levels_;
 }
 
 void MinMaxPyramid::clear() {
-  size_ = 0;
+  count_ = 0;
+  base_ = 0;
   live_levels_ = 1;
-  for (auto& lv : levels_) lv.clear();
-  for (auto& s : sums_) s.clear();
-  for (auto& s : sumsqs_) s.clear();
+  levels_.resize(1);
+  levels_[0].entries.clear();
+  levels_[0].base = 0;
+  pending_ = Entry{};
 }
 
-std::span<const MinMax> MinMaxPyramid::level(u32 l) const {
-  if (l >= level_count()) return {};
-  return levels_[l];
+u64 MinMaxPyramid::level_base(u32 l) const noexcept {
+  return l < levels_.size() ? levels_[l].base : u64{0};
 }
 
+u64 MinMaxPyramid::level_size(u32 l) const noexcept {
+  return l < levels_.size() ? static_cast<u64>(levels_[l].entries.size()) : u64{0};
+}
+
+MinMax MinMaxPyramid::bucket(u32 l, u64 i) const { return at(l, i).mm; }
+
 Range MinMaxPyramid::reduce_buckets(u64 begin, u64 end) const {
-  const u64 e = std::min(end, size_);
-  const u64 b = std::min(begin, e);
-  const u64 b0 = ceil_to_bucket(b) / kBucket;   // first whole bucket inside
-  const u64 b1 = e / kBucket;                   // one past the last whole bucket
+  const u64 e = std::min(end, size());
+  if (begin >= e) return Range{0.0, 0.0};
+  // The bucket grid is absolute while these are window coordinates: window index
+  // i is absolute window_base() + i, so the first whole bucket inside the range is
+  // the first absolute bucket boundary at or after that.
+  const u64 b0 = ceil_to_bucket(base_ + begin) / kBucket;
+  const u64 b1 = (base_ + e) / kBucket;
   if (b1 <= b0) return Range{0.0, 0.0};
   return fold_range(*this, b0, b1);
 }
 
 f64 MinMaxPyramid::sum_buckets(u64 begin, u64 end) const {
-  const u64 e = std::min(end, size_);
-  const u64 b = std::min(begin, e);
-  const u64 b0 = ceil_to_bucket(b) / kBucket;
-  const u64 b1 = e / kBucket;
+  const u64 e = std::min(end, size());
+  if (begin >= e) return 0.0;
+  const u64 b0 = ceil_to_bucket(base_ + begin) / kBucket;
+  const u64 b1 = (base_ + e) / kBucket;
   if (b1 <= b0) return 0.0;
   f64 total = 0.0;
-  cover_buckets(*this, b0, b1, [&](u32 l, u64 i) {
-    const f64 prev = i == 0 ? 0.0 : sums_[l][static_cast<usize>(i - 1)];
-    total += sums_[l][static_cast<usize>(i)] - prev;
-  });
+  cover_buckets(*this, b0, b1, [&](u32 l, u64 i) { total += at(l, i).sum; });
   return total;
 }
 
 f64 MinMaxPyramid::sumsq_buckets(u64 begin, u64 end) const {
-  const u64 e = std::min(end, size_);
-  const u64 b = std::min(begin, e);
-  const u64 b0 = ceil_to_bucket(b) / kBucket;
-  const u64 b1 = e / kBucket;
+  const u64 e = std::min(end, size());
+  if (begin >= e) return 0.0;
+  const u64 b0 = ceil_to_bucket(base_ + begin) / kBucket;
+  const u64 b1 = (base_ + e) / kBucket;
   if (b1 <= b0) return 0.0;
   f64 total = 0.0;
-  cover_buckets(*this, b0, b1, [&](u32 l, u64 i) {
-    const f64 prev = i == 0 ? 0.0 : sumsqs_[l][static_cast<usize>(i - 1)];
-    total += sumsqs_[l][static_cast<usize>(i)] - prev;
-  });
+  cover_buckets(*this, b0, b1, [&](u32 l, u64 i) { total += at(l, i).sumsq; });
   return total;
 }
 
@@ -229,7 +264,7 @@ u32 MinMaxPyramid::level_for(u64 n, f64 samples_per_pixel) const {
   const f64 lg = std::floor(std::log2(ratio));
   u32 l = lg >= f64(62) ? 62u : static_cast<u32>(lg);
   while (l > 0) {
-    const bool exists = l < level_count() && level(l).size() >= 2;
+    const bool exists = l < level_count() && level_size(l) >= 2;
     if (exists && buckets_for(n, l) >= 2) break;
     --l;
   }
@@ -237,14 +272,14 @@ u32 MinMaxPyramid::level_for(u64 n, f64 samples_per_pixel) const {
 }
 
 u64 MinMaxPyramid::snap(f64 x, f64 x0, f64 dx) const {
-  if (dx <= 0.0 || size_ == 0) return 0;
+  if (dx <= 0.0 || size() == 0) return 0;
   const f64 i = (x - x0) / dx;
   // Bound the round before it: llround() is undefined for values a long long
   // cannot hold, and this also maps NaN to index 0.
   if (!(i > 0.0)) return 0;
-  if (i >= f64(size_)) return size_ - 1;
+  if (i >= f64(size())) return size() - 1;
   const u64 idx = static_cast<u64>(std::llround(i));
-  return idx >= size_ ? size_ - 1 : idx;
+  return idx >= size() ? size() - 1 : idx;
 }
 
 }  // namespace plot::data

src/data/series.cpp

@@ -12,23 +12,30 @@ constexpr u64 kGatherChunk = 256;
 
 }  // namespace
 
-Series::QueryParts Series::split_query(u64 begin, u64 end) {
+Series::QueryParts Series::split_query(u64 begin, u64 end) const {
   QueryParts p;
-  // First level-0 bucket boundary at or after begin, and the last at or before
-  // end: [interior_begin, interior_end) is exactly the part the pyramid can
-  // answer with whole buckets.
-  const u64 up = (begin / kBucket + (begin % kBucket == 0 ? u64{0} : u64{1})) * kBucket;
-  const u64 down = (end / kBucket) * kBucket;
+  // The pyramid's buckets are absolute while these are window coordinates, so its
+  // level-0 boundaries sit at window index `window_base() rounded up to the next
+  // multiple of kBucket`, and every kBucket after that. Align the split in
+  // absolute coordinates and come back to the window: aligning in window
+  // coordinates would treat index 0 as a boundary and, for a window that slid
+  // into the middle of a bucket, route samples through the pyramid that it does
+  // not cover.
+  const u64 origin = pyramid().window_base();
+  const u64 a_begin = origin + begin;
+  const u64 a_end = origin + end;
+  const u64 up = (a_begin / kBucket + (a_begin % kBucket == 0 ? u64{0} : u64{1})) * kBucket;
+  const u64 down = (a_end / kBucket) * kBucket;
   if (up < down) {
-    p.interior_begin = up;
-    p.interior_end = down;
+    p.interior_begin = up - origin;   // up >= a_begin >= origin
+    p.interior_end = down - origin;
   }
   // The two edge spans never overlap and never exceed one bucket each: when the
   // interior is empty they tile [begin, end) together, otherwise they are the
   // head and tail buckets half inside the range.
   p.left_begin = begin;
-  p.left_end = std::min(end, up);
-  p.right_begin = std::max(down, p.left_end);
+  p.left_end = std::min(end, up - origin);
+  p.right_begin = std::max(down > origin ? down - origin : u64{0}, p.left_end);
   p.right_end = end;
   return p;
 }
@@ -132,17 +139,25 @@ void Series::gather_impl(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy
     return;
   }
 
-  // Level >= 1: one envelope pair per bucket, x at the bucket's first sample
-  // (min) and at its last sample (max), which keeps x monotonic while covering
-  // the bucket's span.
+  // Level >= 1: one envelope pair per *retained* bucket the range overlaps, x at
+  // the bucket's first sample (min) and at its last sample (max), which keeps x
+  // monotonic while covering the bucket's span. The pyramid's buckets are
+  // absolute, so map the window range onto its grid and clamp to the buckets that
+  // are both complete and wholly inside the window: a bucket that is only partly
+  // retained aggregates samples the window no longer has, and a partial trailing
+  // bucket is not stored at all.
   const u64 span = u64{kBucket} << level;
-  const std::span<const MinMax> buckets = pyramid().level(level);
-  const u64 first = b / span;
-  const u64 last = std::min<u64>((e - 1) / span + 1, static_cast<u64>(buckets.size()));
+  const u64 origin = pyramid().window_base();
+  const u64 lbase = pyramid().level_base(level);
+  const u64 lend = lbase + pyramid().level_size(level);
+  if (lbase >= lend) return;
+  const u64 a_end = origin + e;
+  const u64 first = std::max((origin + b) / span, lbase);
+  const u64 last = std::min((a_end - 1) / span + 1, lend);
   for (u64 bi = first; bi < last; ++bi) {
-    const MinMax m = buckets[static_cast<usize>(bi)];
-    const u64 first_sample = bi * span;
-    const u64 last_sample = std::min(first_sample + span, n) - 1;
+    const MinMax m = pyramid().bucket(level, bi);
+    const u64 first_sample = bi * span - origin;   // >= 0: stored buckets start inside the window
+    const u64 last_sample = std::min((bi + 1) * span, a_end) - 1 - origin;
     out_xy.push_back(f32(x_0 + f64(first_sample) * step));
     out_xy.push_back(m.min);
     out_xy.push_back(f32(x_0 + f64(last_sample) * step));

src/data/stream_series.cpp

@@ -6,14 +6,18 @@
 namespace plot::data {
 namespace {
 
-/// Samples copied per ring read on the ingest path, so rebuilding a saturated
-/// window costs no allocation.
+/// Samples copied per ring read on the ingest path, so appending the samples
+/// produced between two frames costs no allocation.
 constexpr u64 kReadChunk = 256;
 
 }  // namespace
 
 StreamSeries::StreamSeries(u64 capacity, f64 x0, f64 dx)
-    : ring_(capacity), x0_(x0), dx_(dx) {}
+    : ring_(capacity), x0_(x0), dx_(dx) {
+  // Size the pyramid's level table for a full window up front: the ring never
+  // holds more than capacity() samples, so appending never grows it.
+  pyramid_.reserve(capacity);
+}
 
 void StreamSeries::push(f32 y) { ring_.push(y); }
 
@@ -27,62 +31,35 @@ void StreamSeries::acquire() {
   const u64 p = ring_.produced();
   const u64 cap = ring_.capacity();
   const u64 base = p > cap ? p - cap : 0;   // oldest index the ring still holds
-  const u64 n = p - base;                   // retained, published sample count
 
-  if (base != base_) {
-    // The window slid: samples the pyramid covered are gone, and because bucket
-    // boundaries are absolute, extending it incrementally would mis-align every
-    // bucket. Rebuild from the retained samples instead.
-    pyramid_.clear();
-    pyramid_.reserve(n);
-    f32 lo = 0.0f, hi = 0.0f;
-    bool first = true;
+  // Slide the pyramid's window: the buckets that covered samples the ring has
+  // overwritten are dropped, and the rest stay exactly as they were built --
+  // their boundaries are absolute, so nothing has to be recomputed. This is also
+  // where a producer that lapped the consumer by more than the ring holds is
+  // handled: the pyramid restarts at the new base.
+  pyramid_.drop_before(base);
+
+  // Append exactly the samples produced since the last acquire(). Normally that
+  // is one frame's worth; after a lapped producer it is the whole window.
   f32 chunk[kReadChunk];
-    for (u64 i = 0; i < n;) {
-      const u64 take = std::min<u64>(kReadChunk, n - i);
-      ring_.copy_from(base + i, take, chunk);
-      for (u64 k = 0; k < take; ++k) {
-        const f32 v = chunk[k];
-        pyramid_.append(v);
-        if (first) {
-          lo = v;
-          hi = v;
-          first = false;
-        } else {
-          lo = std::min(lo, v);
-          hi = std::max(hi, v);
+  for (u64 a = pyramid_.window_end(); a < p;) {
+    const u64 take = std::min<u64>(kReadChunk, p - a);
+    ring_.copy_from(a, take, chunk);
+    for (u64 k = 0; k < take; ++k) pyramid_.append(chunk[k]);
+    a += take;
   }
-      }
-      i += take;
-    }
-    y_bounds_ = first ? Range{0.0, 0.0} : Range{f64(lo), f64(hi)};
-    base_ = base;
-  } else {
-    // Contiguous: only the samples produced since the last acquire() are new.
-    if (n == 0) y_bounds_ = Range{0.0, 0.0};
-    f32 chunk[kReadChunk];
-    for (u64 i = end_ - base_; i < n;) {
-      const u64 take = std::min<u64>(kReadChunk, n - i);
-      ring_.copy_from(base + i, take, chunk);
-      for (u64 k = 0; k < take; ++k) {
-        const f32 v = chunk[k];
-        pyramid_.append(v);
-        if (i + k == 0) {
-          y_bounds_ = Range{f64(v), f64(v)};
-        } else {
-          y_bounds_.min = std::min(y_bounds_.min, f64(v));
-          y_bounds_.max = std::max(y_bounds_.max, f64(v));
-        }
-      }
-      i += take;
-    }
-  }
-  end_ = p;
+
+  // Exact bounds for the published window, in the same O(log n + kBucket) as any
+  // other exact query over it: the bucket-aligned interior comes from the
+  // pyramid and the two partial edge spans are scanned through copy_raw(). An
+  // incrementally extended bound cannot work here -- it would have to know
+  // whether the extreme it is holding has just slid out of the window.
+  y_bounds_ = reduce(0, size());
 }
 
-u64 StreamSeries::size() const { return end_ - base_; }
+u64 StreamSeries::size() const { return pyramid_.size(); }
 
-f64 StreamSeries::x0() const { return x0_ + f64(base_) * dx_; }
+f64 StreamSeries::x0() const { return x0_ + f64(pyramid_.window_base()) * dx_; }
 
 f64 StreamSeries::dx() const { return dx_; }
 
@@ -105,9 +82,10 @@ void StreamSeries::copy_raw(u64 begin, u64 end, f32* out) const {
   const u64 n = size();
   const u64 b = std::min(begin, n);
   const u64 e = std::min(std::max(end, b), n);
-  // Retained index b is absolute base_ + b: fixed for the whole copy, so a
-  // pushing producer cannot shift the window midway.
-  ring_.copy_from(base_ + b, e - b, out);
+  // Retained index b is absolute window_base() + b: fixed for the whole copy, so
+  // a pushing producer cannot shift the window midway (the pyramid is written by
+  // this thread alone, so its window cannot move under the read either).
+  ring_.copy_from(pyramid_.window_base() + b, e - b, out);
   std::fill(out + static_cast<std::ptrdiff_t>(e - b),
             out + static_cast<std::ptrdiff_t>(want), 0.0f);
 }

tests/CMakeLists.txt

@@ -40,9 +40,10 @@ add_executable(plot_tests
   egl_headless.cpp
 )
 target_link_libraries(plot_tests PRIVATE plot::core ${plot_egl_library} Threads::Threads)
-# Same switch the library is built with: the decomposition-cost test reads the
-# counter behind it (see include/plot/data/detail/cover_count.hpp).
-target_compile_definitions(plot_tests PRIVATE PLOT_PYRAMID_COUNT_COVERS)
+# Same switches the library is built with: the cost tests read the counters
+# behind them (see include/plot/data/detail/{cover,merge}_count.hpp).
+target_compile_definitions(plot_tests PRIVATE PLOT_PYRAMID_COUNT_COVERS
+                                             PLOT_PYRAMID_COUNT_MERGES)
 plot_apply_warnings(plot_tests)
 
 add_test(NAME plot_tests COMMAND plot_tests)

tests/test_minmax_pyramid.cpp

@@ -1,12 +1,36 @@
 #include "harness.hpp"
 #include <plot/data/detail/cover_count.hpp>
+#include <plot/data/detail/merge_count.hpp>
 #include <plot/data/minmax_pyramid.hpp>
+#include <algorithm>
 #include <random>
 
 using plot::data::kBucket;
+using plot::data::MinMax;
 using plot::data::MinMaxPyramid;
 using plot::Range;
 
+namespace {
+
+/// Brute-force aggregate of the absolute span of level-`l` bucket `b`, from the
+/// same value function the pyramid was fed. This is the oracle the absolute
+/// bucket indexing is judged against: a bucket that has slid inside the window
+/// must still aggregate exactly its own absolute samples.
+template <typename ValueFn>
+MinMax brute_bucket(u32 l, u64 b, const ValueFn& value) {
+  const u64 span = u64{kBucket} << l;
+  const u64 first = b * span;
+  MinMax m{value(first), value(first)};
+  for (u64 i = first + 1; i < first + span; ++i) {
+    const f32 v = value(i);
+    m.min = std::min(m.min, v);
+    m.max = std::max(m.max, v);
+  }
+  return m;
+}
+
+}  // namespace
+
 PLOT_TEST(pyramid_bucket_extremes_preserved) {
   MinMaxPyramid p;
   p.reserve(1000);
@@ -107,7 +131,8 @@ PLOT_TEST(pyramid_clear_and_rebuild) {
   // bucket and ask the bucket-grained query for its extrema.
   for (u32 i = 1; i < kBucket; ++i) p.append(1.0f);
   PLOT_CHECK(p.size() == kBucket);
-  PLOT_CHECK(p.level(0).size() == 1);
+  PLOT_CHECK(p.level_base(0) == 0);
+  PLOT_CHECK(p.level_size(0) == 1);
   PLOT_CHECK_NEAR(p.reduce_buckets(0, kBucket).max, 7.0, 1e-6);
   PLOT_CHECK_NEAR(p.reduce_buckets(0, kBucket).min, 1.0, 1e-6);
 }
@@ -121,7 +146,7 @@ PLOT_TEST(pyramid_cover_cost_is_logarithmic_for_unaligned_starts) {
   MinMaxPyramid p;
   p.reserve(1'000'000);
   for (u64 i = 0; i < 1'000'000; ++i) p.append(0.0f);
-  PLOT_CHECK(p.level(0).size() == 1'000'000 / kBucket);   // 15625, no partial bucket
+  PLOT_CHECK(p.level_size(0) == 1'000'000 / kBucket);   // 15625, no partial bucket
 
   auto folds_for = [&](u64 begin, u64 end) {
     plot::data::detail::cover_entry_count().store(0, std::memory_order_relaxed);
@@ -134,3 +159,131 @@ PLOT_TEST(pyramid_cover_cost_is_logarithmic_for_unaligned_starts) {
   PLOT_CHECK(unaligned < 100);
   PLOT_CHECK(unaligned <= u64{4} * aligned);       // misalignment costs entries, not a scan
 }
+
+PLOT_TEST(pyramid_drop_before_slides_the_window) {
+  MinMaxPyramid p;
+  for (u64 i = 0; i < 4096; ++i) p.append(f32(i % 13));
+  PLOT_CHECK(p.window_base() == 0);
+  PLOT_CHECK(p.window_end() == 4096);
+  PLOT_CHECK(p.size() == 4096);
+
+  p.drop_before(1000);
+  PLOT_CHECK(p.window_base() == 1000);
+  PLOT_CHECK(p.size() == 3096);
+  // The window's first *whole* bucket starts at 1024: the bucket the drop cut
+  // into is not representable as a whole bucket and is never queried.
+  PLOT_CHECK(p.level_base(0) == 1024 / kBucket);
+  PLOT_CHECK(p.level_base(0) + p.level_size(0) == 4096 / kBucket);
+
+  f32 lo = 1.0f, hi = -1.0f;
+  for (u64 i = 1024; i < 4096; ++i) {
+    lo = std::min(lo, f32(i % 13));
+    hi = std::max(hi, f32(i % 13));
+  }
+  const Range r = p.reduce_buckets(0, p.size());
+  PLOT_CHECK_NEAR(r.min, lo, 1e-6);
+  PLOT_CHECK_NEAR(r.max, hi, 1e-6);
+  // Window [1000, 1024) holds no whole bucket at all: an empty answer, not one
+  // that quietly reaches into the dropped samples.
+  PLOT_CHECK(p.reduce_buckets(0, 24).span() == 0.0);
+  PLOT_CHECK(p.sum_buckets(0, 24) == 0.0);
+  PLOT_CHECK(p.sumsq_buckets(0, 24) == 0.0);
+
+  p.drop_before(1000);                    // at the base: no-op
+  PLOT_CHECK(p.window_base() == 1000);
+  p.drop_before(4096);                    // at the end: the window is empty
+  PLOT_CHECK(p.size() == 0);
+  p.append(5.0f);                         // and appending starts a fresh window
+  PLOT_CHECK(p.size() == 1);
+  PLOT_CHECK(p.window_base() == 4096);
+}
+
+PLOT_TEST(pyramid_bucket_aggregates_stay_absolute_across_slides) {
+  // The invariant the sliding window rests on: a bucket that has slid inside the
+  // window is never recomputed, so it must already hold the aggregate of its own
+  // absolute span -- at every level, after any number of drops.
+  MinMaxPyramid p;
+  const auto value = [](u64 i) { return f32((i * 37u) % 101u) - 50.0f; };
+  constexpr u64 kTotal = 20'000;
+  constexpr u64 kWindow = 4'000;
+  for (u64 i = 0; i < kTotal; ++i) {
+    p.append(value(i));
+    if ((i + 1) % 997 == 0 && i + 1 > kWindow) p.drop_before(i + 1 - kWindow);
+  }
+  // The last drop is the last multiple of 997 at or below kTotal.
+  PLOT_CHECK(p.window_base() == (kTotal / 997) * 997 - kWindow);
+  for (u32 l = 0; l < p.level_count(); ++l) {
+    PLOT_CHECK(p.level_size(l) > 0);
+    const u64 span = u64{kBucket} << l;
+    for (u64 b = p.level_base(l); b < p.level_base(l) + p.level_size(l); ++b) {
+      const MinMax want = brute_bucket(l, b, value);
+      const MinMax got = p.bucket(l, b);
+      PLOT_CHECK_NEAR(got.min, want.min, 1e-6);
+      PLOT_CHECK_NEAR(got.max, want.max, 1e-6);
+      PLOT_CHECK(b * span >= p.window_base());          // wholly inside the window
+      PLOT_CHECK((b + 1) * span <= p.window_end());     // and complete
+    }
+  }
+}
+
+PLOT_TEST(pyramid_sliding_window_bucket_queries_match_bruteforce) {
+  MinMaxPyramid p;
+  const auto value = [](u64 i) { return f32(i % 89) * 0.25f - 5.0f; };
+  constexpr u64 kTotal = 12'000;
+  constexpr u64 kWindow = 3'000;
+  for (u64 i = 0; i < kTotal; ++i) {
+    p.append(value(i));
+    if ((i + 1) % 613 != 0) continue;
+    const u64 abs0 = i + 1 > kWindow ? i + 1 - kWindow : 0;
+    p.drop_before(abs0);
+    const u64 n = p.size();
+    // Window coordinates: window index j is absolute abs0 + j.
+    const u64 first = abs0 / kBucket + (abs0 % kBucket == 0 ? u64{0} : u64{1});
+    const u64 last = (abs0 + n) / kBucket;
+    if (last <= first) continue;
+    f32 lo = 1e30f, hi = -1e30f;
+    f64 sum = 0.0, sq = 0.0;
+    for (u64 a = first * kBucket; a < last * kBucket; ++a) {
+      const f32 v = value(a);
+      lo = std::min(lo, v);
+      hi = std::max(hi, v);
+      sum += f64(v);
+      sq += f64(v) * f64(v);
+    }
+    const u64 wb = first * kBucket - abs0;
+    const u64 we = last * kBucket - abs0;
+    const Range r = p.reduce_buckets(wb, we);
+    PLOT_CHECK_NEAR(r.min, lo, 1e-6);
+    PLOT_CHECK_NEAR(r.max, hi, 1e-6);
+    PLOT_CHECK_NEAR(p.sum_buckets(wb, we), sum, 1e-3);
+    PLOT_CHECK_NEAR(p.sumsq_buckets(wb, we), sq, 1e-1);
+  }
+}
+
+PLOT_TEST(pyramid_append_cost_is_amortised_constant) {
+  // A sample must not walk the live levels: level l gains an entry once per
+  // kBucket << l samples, so N appends perform ~N/32 merges however many levels
+  // the pyramid holds. Walking every level per append costs ~N * levels.
+  MinMaxPyramid p;
+  p.reserve(1u << 20);
+  constexpr u64 kAppends = 1u << 20;
+  for (u64 i = 0; i < kAppends; ++i) p.append(0.5f);
+  PLOT_CHECK(p.level_count() >= 10);   // 2^20 samples: 16384 level-0 buckets
+
+  plot::data::detail::merge_count().store(0, std::memory_order_relaxed);
+  for (u64 i = 0; i < kAppends; ++i) p.append(0.5f);
+  const u64 merges = plot::data::detail::merge_count().load(std::memory_order_relaxed);
+  // ~N/64 + N/128 + ... = ~N/32; the bound leaves 2x room, and is four orders of
+  // magnitude below the N * live_levels an unbounded walk would perform.
+  PLOT_CHECK(merges <= kAppends / 16);
+
+  // Sliding must not add per-sample work either: the appends below run against a
+  // window whose base moves with every sample.
+  plot::data::detail::merge_count().store(0, std::memory_order_relaxed);
+  for (u64 i = 0; i < kAppends; ++i) {
+    p.drop_before(i + 1);
+    p.append(0.5f);
+  }
+  const u64 slid = plot::data::detail::merge_count().load(std::memory_order_relaxed);
+  PLOT_CHECK(slid <= kAppends / 16);
+}

tests/test_series.cpp

@@ -1,13 +1,18 @@
 #include "harness.hpp"
 #include <plot/data/array_series.hpp>
+#include <plot/data/detail/merge_count.hpp>
 #include <plot/data/stream_series.hpp>
 #include <algorithm>
+#include <array>
 #include <atomic>
+#include <chrono>
 #include <cmath>
 #include <random>
 #include <thread>
 #include <vector>
 
+using plot::data::kBucket;
+
 PLOT_TEST(array_series_bounds_and_gather) {
   std::vector<f32> y{1, 5, -2, 3};
   plot::data::ArraySeries s(std::move(y), /*x0=*/10.0, /*dx=*/0.5);
@@ -159,3 +164,184 @@ PLOT_TEST(stream_series_push_and_read_are_race_free) {
   PLOT_CHECK(reads >= 1);
   PLOT_CHECK(sizes_ok);
 }
+
+namespace {
+
+/// Buckets the pyramid holds across every level: its footprint, not its window.
+u64 pyramid_entries(const plot::data::MinMaxPyramid& p) {
+  u64 total = 0;
+  for (u32 l = 0; l < p.level_count(); ++l) total += p.level_size(l);
+  return total;
+}
+
+}  // namespace
+
+PLOT_TEST(stream_series_sliding_window_queries_match_bruteforce) {
+  // After the base has moved many times, an exact query must still match a scan
+  // of exactly the retained samples. The pyramid's buckets live in absolute
+  // sample space while the window's base is arbitrary, and that meeting point is
+  // where an off-by-one hides -- so test the sliding case, not just the static
+  // ArraySeries one.
+  constexpr u64 kCapacity = 1u << 14;
+  constexpr u64 kPushes = 60'000;
+  const auto value = [](u64 i) { return f32((i * 29u) % 173u) - 86.0f; };
+  plot::data::StreamSeries s(kCapacity, 0.0, 1e-6);
+  for (u64 i = 0; i < kPushes; i += 337) {
+    const u64 n = std::min<u64>(337, kPushes - i);
+    for (u64 k = 0; k < n; ++k) s.push(value(i + k));
+    s.acquire();   // the window's base moves on every one of these
+  }
+
+  const u64 n = s.size();
+  const u64 base = s.produced() - n;
+  PLOT_CHECK(n == kCapacity);
+  PLOT_CHECK(base > 2 * kCapacity);             // the window really did slide
+  PLOT_CHECK(s.pyramid().size() == n);          // pyramid() indexes the window
+  PLOT_CHECK(s.pyramid().window_base() == base);
+  PLOT_CHECK(s.pyramid().window_end() == s.produced());
+  PLOT_CHECK_NEAR(s.x0(), f64(base) * 1e-6, 1e-12);
+  PLOT_CHECK(s.x_bounds().min == s.x0());
+  PLOT_CHECK_NEAR(s.x_bounds().max, f64(base + n - 1) * 1e-6, 1e-9);
+
+  // Brute force in window coordinates over the retained samples only.
+  const auto brute = [&](u64 a, u64 b) {
+    f64 lo = f64(value(base + a)), hi = lo;
+    f64 sum = 0.0, sq = 0.0;
+    for (u64 i = a; i < b; ++i) {
+      const f64 v = f64(value(base + i));
+      lo = std::min(lo, v);
+      hi = std::max(hi, v);
+      sum += v;
+      sq += v * v;
+    }
+    return std::array<f64, 4>{lo, hi, sum, sq};
+  };
+
+  const u64 starts[] = {0, 1, 63, 64, 65, 1000, 7919, n - 200};
+  for (const u64 a : starts) {
+    for (u64 b = a + 1; b <= n; b += 1301) {
+      const std::array<f64, 4> want = brute(a, b);
+      const plot::Range r = s.reduce(a, b);
+      PLOT_CHECK_NEAR(r.min, want[0], 1e-4);
+      PLOT_CHECK_NEAR(r.max, want[1], 1e-4);
+      PLOT_CHECK_NEAR(s.sum(a, b), want[2], 1e-2);
+      PLOT_CHECK_NEAR(s.sumsq(a, b), want[3], 1e-1);
+    }
+  }
+  const std::array<f64, 4> whole = brute(0, n);
+  PLOT_CHECK_NEAR(s.y_bounds().min, whole[0], 1e-6);
+  PLOT_CHECK_NEAR(s.y_bounds().max, whole[1], 1e-6);
+
+  // The level accessors are in absolute bucket coordinates: a stored bucket must
+  // aggregate its own absolute span, the sliding window included.
+  const u64 span = u64{kBucket} << 1;
+  const u64 lbase = s.pyramid().level_base(1);
+  const u64 lsize = s.pyramid().level_size(1);
+  PLOT_CHECK(lsize >= 2);
+  for (u64 b = lbase; b < lbase + std::min<u64>(lsize, 4); ++b) {
+    const std::array<f64, 4> want = brute(b * span - base, (b + 1) * span - base);
+    const plot::data::MinMax m = s.pyramid().bucket(1, b);
+    PLOT_CHECK_NEAR(m.min, want[0], 1e-6);
+    PLOT_CHECK_NEAR(m.max, want[1], 1e-6);
+  }
+
+  // level-1 gather: one envelope pair per retained bucket the range overlaps, x
+  // at the bucket's own first and last sample. This is the mapping the renderer
+  // draws from.
+  std::vector<f32> out;
+  s.gather(1, 0, n, out);
+  const u64 first = std::max(base / span, lbase);
+  const u64 last = std::min((base + n - 1) / span + 1, lbase + lsize);
+  PLOT_CHECK(out.size() == 4 * (last - first));
+  for (u64 bi = first; bi < last; ++bi) {
+    const std::array<f64, 4> want = brute(bi * span - base, (bi + 1) * span - base);
+    const plot::usize k = static_cast<plot::usize>(bi - first);
+    const u64 first_sample = bi * span - base;
+    const u64 last_sample = std::min((bi + 1) * span, base + n) - 1 - base;
+    // x is in data coordinates: x0() is the retained window's first sample, so
+    // window index j plots at (base + j) * dx.
+    PLOT_CHECK_NEAR(out[4 * k], f32(f64(base + first_sample) * 1e-6), 1e-9);
+    PLOT_CHECK_NEAR(out[4 * k + 1], want[0], 1e-6);
+    PLOT_CHECK_NEAR(out[4 * k + 2], f32(f64(base + last_sample) * 1e-6), 1e-9);
+    PLOT_CHECK_NEAR(out[4 * k + 3], want[1], 1e-6);
+  }
+}
+
+PLOT_TEST(stream_series_steady_state_acquire_is_proportional_to_produced) {
+  // The defect this pins: a saturated ring whose base moved every frame used to
+  // rebuild the whole window, costing O(capacity * live_levels) merges per
+  // acquire. It must cost O(samples produced since the last acquire) instead, so
+  // the same production through a 16x larger window must cost the same.
+  const auto merges_for = [](u64 capacity) {
+    plot::data::StreamSeries s(capacity, 0.0, 1.0);
+    constexpr u64 kSaturate = 1u << 20;
+    for (u64 i = 0; i < kSaturate; ++i) s.push(f32(i % 977));
+    s.acquire();
+    PLOT_CHECK(s.size() == capacity);
+
+    constexpr u64 kFrames = 64;
+    constexpr u64 kFrame = 1u << 13;   // 8192 samples: 1 MS/s at ~122 fps
+    plot::data::detail::merge_count().store(0, std::memory_order_relaxed);
+    for (u64 f = 0; f < kFrames; ++f) {
+      for (u64 k = 0; k < kFrame; ++k) s.push(f32((kSaturate + f * kFrame + k) % 977));
+      s.acquire();
+    }
+    return plot::data::detail::merge_count().load(std::memory_order_relaxed);
+  };
+
+  constexpr u64 kProduced = 64 * (1u << 13);
+  const u64 small = merges_for(1u << 16);   // 64k-sample window
+  const u64 big = merges_for(1u << 20);     // 1M-sample window: 16x to rebuild
+  // ~kProduced/32 in practice; rebuilding the 1M window alone would merge
+  // kCapacity/64 * live_levels ~ 245'000 buckets per acquire.
+  PLOT_CHECK(small <= kProduced / 16);
+  PLOT_CHECK(big <= kProduced / 16);
+  PLOT_CHECK(big <= 2 * small + kBucket);
+}
+
+PLOT_TEST(stream_series_steady_state_acquire_is_fast) {
+  // Wall-clock backstop for the merge count above: rebuilding the 1M-sample
+  // window measured ~44 ms, so 128 such frames would need ~5.6 s. The sliding
+  // path does the same work in a few milliseconds; the bound is two orders of
+  // magnitude clear of both, so it is not a thin timing margin.
+  plot::data::StreamSeries s(1u << 20, 0.0, 1.0);
+  constexpr u64 kSaturate = 1u << 20;
+  for (u64 i = 0; i < kSaturate; ++i) s.push(f32(i % 977));
+  s.acquire();
+
+  constexpr u64 kFrames = 128;
+  constexpr u64 kFrame = 1u << 13;
+  const auto t0 = std::chrono::steady_clock::now();
+  for (u64 f = 0; f < kFrames; ++f) {
+    for (u64 k = 0; k < kFrame; ++k) s.push(f32((kSaturate + f * kFrame + k) % 977));
+    s.acquire();
+  }
+  const f64 ms =
+      std::chrono::duration<f64>(std::chrono::steady_clock::now() - t0).count() * 1.0e3;
+  PLOT_CHECK(s.size() == 1u << 20);
+  PLOT_CHECK(ms < 250.0);
+}
+
+PLOT_TEST(stream_series_pyramid_memory_is_bounded_by_the_window) {
+  // 50M samples through a 1M-sample ring: the pyramid's footprint must track the
+  // retained window (n/64 level-0 buckets plus the levels over them), not the
+  // samples ever pushed.
+  constexpr u64 kCapacity = 1u << 20;
+  constexpr u64 kTotal = 50u * (1u << 20);
+  constexpr u64 kChunk = 1u << 19;
+  plot::data::StreamSeries s(kCapacity, 0.0, 1.0);
+  u64 entries_after_10m = 0;
+  for (u64 p = 0; p < kTotal; p += kChunk) {
+    for (u64 i = 0; i < kChunk; ++i) s.push(f32((p + i) % 251));
+    s.acquire();
+    if (p + kChunk == 10u * (1u << 20)) entries_after_10m = pyramid_entries(s.pyramid());
+  }
+  const u64 entries = pyramid_entries(s.pyramid());
+  const u64 bound = 2 * (kCapacity / kBucket) + kBucket;
+  PLOT_CHECK(s.produced() == kTotal);
+  PLOT_CHECK(s.size() == kCapacity);
+  PLOT_CHECK(entries <= bound);
+  // 5x the samples pushed, same footprint: levels deeper than one chunk can
+  // differ by a bucket each, hence the slack.
+  PLOT_CHECK(entries <= entries_after_10m + kBucket);
+}